Упр.356 ГДЗ Колягин Ткачёва 7 класс (Алгебра)

1. $$\frac{81\cdot 27^3}{3^8}=\frac{3^4\cdot (3^3)^3}{3^8}=\frac{3^4\cdot 3^9}{3^8}=3^{4+9-8}=3^5=243.$$
2. $$\frac{2^8\cdot (7^2)^4}{14^7}=\frac{2^8\cdot 7^8}{(2\cdot 7)^7}=\frac{2^8\cdot 7^8}{2^7\cdot 7^7}=2^{8-7}\cdot 7^{8-7}=14.$$
3. $$\frac{16^2\cdot 3^5}{12^4}=\frac{(4^2)^2\cdot 3^5}{(4\cdot 3)^4}=\frac{4^4\cdot 3^5}{4^4\cdot 3^4}=3.$$
4. $$\frac{2^9\cdot (2^2)^5}{(2^5)^3}=\frac{2^9\cdot 2^{10}}{2^{15}}=2^{9+10-15}=2^4=16.$$

5. $$(2b+a)(2b-a)=(2b)^2-a^2=4b^2-a^2.$$
6. $$(c+3d)(c-3d)=c^2-(3d)^2=c^2-9d^2.$$
7. $$(y+6x)(6x-y)=(6x+y)(6x-y)=(6x)^2-y^2=36x^2-y^2.$$
8. $$(3m-2n)(2n+3m)=(3m-2n)(3m+2n)=(3m)^2-(2n)^2=9m^2-4n^2.$$

Ответ

1) $$243$$; 2) $$14$$; 3) $$3$$; 4) $$16$$; 5) $$4b^2-a^2$$; 6) $$c^2-9d^2$$; 7) $$36x^2-y^2$$; 8) $$9m^2-4n^2$$.